High accuracy of Karplus equations for relating three-bond J couplings to protein backbone torsion angles

Structure-Based Experimental Datasets for Benchmarking Protein Simulation Force Fields [Article v0.1]

This review article provides an overview of structurally oriented experimental datasets that can be used to benchmark protein force fields, focusing on data generated by nuclear magnetic resonance (NMR) spectroscopy and room temperature (RT) protein crystallography. We discuss what the observables are, what they tell us about structure and dynamics, what makes them useful for assessing force field accuracy, and how they can be connected to molecular dynamics simulations carried out using the force field one wishes to benchmark. We also touch on statistical issues that arise when comparing simulations with experiment. We hope this article will be particularly useful to computational researchers and trainees who develop, benchmark, or use protein force fields for molecular simulations.

Determining accurate conformational ensembles of intrinsically disordered proteins at atomic resolution

Determining accurate atomic resolution conformational ensembles of intrinsically disordered proteins (IDPs) is extremely challenging. Molecular dynamics (MD) simulations provide atomistic conformational ensembles of IDPs, but their accuracy is highly dependent on the quality of physical models, or force fields, used. Here, we demonstrate how to determine accurate atomic resolution conformational ensembles of IDPs by integrating all-atom MD simulations with experimental data from nuclear magnetic resonance (NMR) spectroscopy and small-angle x-ray scattering (SAXS) with a simple, robust and fully automated maximum entropy reweighting procedure. We demonstrate that when this approach is applied with sufficient experimental data, IDP ensembles derived from different MD force fields converge to highly similar conformational distributions. The maximum entropy reweighting procedure presented here facilitates the integration of MD simulations with extensive experimental datasets and enables the calculation of accurate, force-field independent atomic resolution conformational ensembles of IDPs.

The Open Force Field Initiative: Open Software and Open Science for Molecular Modeling

Force fields are a key component of physics-based molecular modeling, describing the energies and forces in a molecular system as a function of the positions of the atoms and molecules involved. Here, we provide a review and scientific status report on the work of the Open Force Field (OpenFF) Initiative, which focuses on the science, infrastructure and data required to build the next generation of biomolecular force fields. We introduce the OpenFF Initiative and the related OpenFF Consortium, describe its approach to force field development and software, and discuss accomplishments to date as well as future plans. OpenFF releases both software and data under open and permissive licensing agreements to enable rapid application, validation, extension, and modification of its force fields and software tools. We discuss lessons learned to date in this new approach to force field development. We also highlight ways that other force field researchers can get involved, as well as some recent successes of outside researchers taking advantage of OpenFF tools and data.

Ensemble determination by NMR data deconvolution

Nuclear magnetic resonance (NMR) is the spectroscopic technique of choice for determining molecular conformations in solution at atomic resolution. As solution NMR spectra are rich in structural and dynamic information, the way in which the data should be acquired and handled to deliver accurate ensembles is not trivial. This Review provides a guide to the NMR experiment selection and parametrization process, the generation of viable theoretical conformer pools and the deconvolution of time-averaged NMR data into a conformer ensemble that accurately represents a flexible molecule in solution. In addition to reviewing the key elements of solution ensemble determination of flexible mid-sized molecules, the feasibility and pitfalls of data deconvolution are discussed with a comparison of the performance of representative algorithms.

High-resolution NMR spectroscopy for measuring complex samples based on chemical-shift-difference selection

NMR spectroscopy serves as an immensely powerful tool for component assignments and molecular structure elucidations. However, proton NMR spectra are generally trapped with spectral congestion caused by limited frequency differences and complex multiplets. 2D NMR can effectively relieve spectral congestion, but its resolution and acquisition efficiency are restricted by the broad spectral bandwidth. Herein, we introduce an NMR method based on chemical-shift-difference selection by chirp excitation to record high-resolution 2D NMR spectra for extracting coupling correlation networks and multiplet structures, suitable for measurements on complex samples. The performance of the proposed method is illustrated in determining diastereotopic methylene protons, small frequency-difference coupled proton pairs of furanose, pyranose and benzene rings. This study is expected to benefit molecular structure elucidation and composition analysis of complex samples in chemistry, biochemistry and metabonomics.

Measuring the 3J HNHa coupling by a simple 2D-intra-HNCA IP/AP-E.COSY with simultaneous encoding of 15N chemical shift and 1J HaCa evolution

The ³J coupling values are commonly used in biomolecular NMR to extract structural information. Here we present a novel intra HNCA IP/AP E.COSY pulse sequence that allows to measure ³J H^NH^a coupling constants by a simple and rapid two-dimensional ¹H-¹⁵N correlation experiment where the ¹⁵N frequency is encoded at the same time as the ¹J H^aC^a coupling evolution. The advantage with respect to the conventional 3D HNCA E.COSY pulse sequence is the dimensionality reduction to a simple 2D experiment, which decreases acquisition time and facilitates data analysis. The performance of this new experiment is demonstrated with an ubiquitin sample at 500 MHz.

Characterization of Amyloidogenic Peptide Aggregability in Helical Subspace

Prototypical amyloidogenic peptides amyloid-β (Aβ) and α-synuclein (αS) can undergo helix-helix associations via partially folded helical conformers, which may influence pathological progression to Alzheimer's (AD) and Parkinson's disease (PD), respectively. At the other extreme, stable folded helical conformers have been reported to resist self-assembly and amyloid formation. Experimental characterisation of such disparities in aggregation profiles due to subtle differences in peptide stabilities is precluded by the conformational heterogeneity of helical subspace. The diverse physical models used in molecular simulations allow sampling distinct regions of the phase space and are extensive in capturing the ensemble of rich helical subspace. Robust and powerful computational predictive methods utilizing network theory and free energy mapping can model the origin of helical population shifts in amyloidogenic peptides, which highlight their inherent aggregability. In this chapter, we discuss computational models, methods, design rules, and strategies to identify the driving force behind helical self-assembly and the molecular origin of aggregation resistance in helical intermediates of Aβ42 and αS. By extensive multiscale mapping of intrapeptide interactions, we show that the computational models can capture features that are otherwise imperceptible to experiments. Our models predict that targeting terminal residues may allow modulation and control of initial pathogenic aggregability of amyloidogenic peptides.

Two-bond 13C-13C spin-coupling constants in saccharides: dependencies on exocyclic hydroxyl group conformation

Seven doubly ¹³C-labeled isotopomers of methyl β-D-glucopyranoside, methyl β-D-xylopyranoside, methyl β-D-galactopyranoside, methyl β-D-galactopyranosyl-(1→4)-β-D-glucopyranoside and methyl β-D-galactopyranosyl-(1→4)-β-D-xylopyranoside were prepared, crystallized, and studied by single-crystal X-ray crystallography and solid-state ¹³C NMR spectroscopy to determine experimentally the dependence of ²J_C1,C3 values in aldopyranosyl rings on the C1-C2-O2-H torsion angle, θ₂, involving the C2 carbon of the C1-C2-C3 coupling pathway. Using X-ray crystal structures to determine θ₂ in crystalline samples and by selecting compounds that exhibit a relatively wide range of θ₂ values in the crystalline state, ²J_C1,C3 values measured in crystalline samples were plotted against θ₂ and the resulting plot compared to that obtained from density functional theory (DFT) calculations. For θ₂ values ranging from ∼90° to ∼240°, very good agreement was observed between the experimental and theoretical plots, providing strong validation of DFT-calculated spin-coupling dependencies on exocyclic C-O bond conformation involving the central carbon of geminal C-C-C coupling pathways. These findings provide new experimental evidence supporting the use of ²J_CCC values as non-conventional spin-coupling constraints in MA'AT conformational modeling of saccharides in solution, and the use of NMR spin-couplings not involving coupled hydroxyl hydrogens as indirect probes of C-O bond conformation. Solvomorphism was observed in crystalline βGal-(1→4)-βGlcOCH₃ wherein the previously-reported methanol solvate form was found to spontaneously convert to a monohydrate upon air-drying, leading to small but discernible conformational changes in, and a new crystalline form of, this disaccharide.

Predicting scalar coupling constants by graph angle-attention neural network

Scalar coupling constant (SCC), directly measured by nuclear magnetic resonance (NMR) spectroscopy, is a key parameter for molecular structure analysis, and widely used to predict unknown molecular structure. Restricted by the high cost of NMR experiments, it is impossible to measure the SCC of unknown molecules on a large scale. Using density functional theory (DFT) to theoretically calculate the SCC of molecules is incredibly challenging, due to the cost of substantial computational time and space. Graph neural networks (GNN) of artificial intelligence (AI) have great potential in constructing molecul ar-like topology models, which endows them the ability to rapidly predict SCC through data-driven machine learning methods, and avoiding time-consuming quantum chemical calculations. With a priori knowledge of angles, we propose a graph angle-attention neural network (GAANN) model to predict SCC by means of some easily accessible related information. GAANN, with a multilayer message-passing network and a self-attention mechanism, can accurately simulate the molecular-like topological structure and predict molecular properties. Our simulations show that the prediction accuracy by GAANN, with the log(MAE) = −2.52, is close to that by DFT calculations. Different from conventional AI methods, GAANN combining the AI method with quantum chemistry theory (Karplus equation) has a strong physicochemical interpretability about angles. From an AI perspective, we find that bond angle has the highest correlation with the SCC among all angle features (dihedral angle, bond angle, geometric angles) about multiple coupling types in the small molecule datasets.

Computational approaches to amino acid side-chain conformation using combined NMR theoretical and experimental results: leucine-67 in Desulfovibrio vulgaris flavodoxin

In this paper, we show that the combination of NMR theoretical and experimental results can help to solve the molecular structure of peptides, here it is used as an example the residue Leucine-67 in Desulfovibrio vulgaris flavodoxin. We apply a computational protocol based on the leucine amino acid dipeptide, which, using calculated and experimental spin-spin coupling constants, allows us to obtain the conformation of the amino acid side chain. Calculated results show that the best agreement is obtained when three conformers around the lateral chain angle $\chi _1$ are considered or when the dynamic effect in the torsional angles is included. The population of each structure is estimated and analyzed according to the correlation between those two approaches. Independently of the approach, the estimated $\chi _1$ angle in solution is close to the staggered value of -60$^\circ $ and deviates significantly from the average x-ray angle of -90$^\circ $.

The Ambivalent Role of Proline Residues in an Intrinsically Disordered Protein: From Disorder Promoters to Compaction Facilitators

Intrinsically disordered proteins (IDPs) carry out many biological functions. They lack a stable three-dimensional structure, but rather adopt many different conformations in dynamic equilibrium. The interplay between local dynamics and global rearrangements is key for their function. In IDPs, proline residues are significantly enriched. Given their unique physicochemical and structural properties, a more detailed understanding of their potential role in stabilizing partially folded states in IDPs is highly desirable. Nuclear magnetic resonance (NMR) spectroscopy, and in particular ¹³C-detected NMR, is especially suitable to address these questions. We applied a ¹³C-detected strategy to study Osteopontin, a largely disordered IDP with a central compact region. By using the exquisite sensitivity and spectral resolution of these novel techniques, we gained unprecedented insight into cis-Pro populations, their local structural dynamics, and their role in mediating long-range contacts. Our findings clearly call for a reassessment of the structural and functional role of proline residues in IDPs. The emerging picture shows that proline residues have ambivalent structural roles. They are not simply disorder promoters but rather can, depending on the primary sequence context, act as nucleation sites for structural compaction in IDPs. These unexpected features provide a versatile mechanistic toolbox to enrich the conformational ensembles of IDPs with specific features for adapting to changing molecular and cellular environments.

Fluoro-Aryl Substituted α,β2,3-Peptides in the Development of Foldameric Antiparallel β-Sheets: A Conformational Study

α,β2,3-Disteroisomeric foldamers of general formula Boc(S-Ala-β-2R,3R-Fpg)nOMe or Boc(S-Ala-β-2S,3S-Fpg)nOMe were prepared from both enantiomers of syn H-2-(2-F-Phe)-h-PheGly-OH (named β-Fpg) and S-alanine. Our peptides show two appealing features for biomedical applications: the presence of fluorine, attractive for non-covalent interactions, and aryl groups, crucial for π-stacking. A conformational study was performed, using IR, NMR and computational studies of diastereoisomeric tetra- and hexapeptides containing the β2,3-amino acid in the R,R- and S,S-stereochemistry, respectively. We found that the stability of peptide conformation is dependent on the stereochemistry of the β-amino acid. Combining S-Ala with β-2R,3R-Fpg, a stable extended β-strand conformation was obtained. Furthermore, β-2R,3R-Fpg containing hexapeptide self-assembles to form antiparallel β-sheet structure stabilized by intermolecular H-bonds and π,π-interactions. These features make peptides containing the β2,3-fluoro amino acid very appealing for the development of bioactive proteolytically stable foldameric β-sheets as modulators of protein-protein interaction (PPI).

From glucose to enantiopure morpholino β-amino acid: a new tool for stabilizing γ-turns in peptides

“Environmentally sustainable” synthesis of a new enantiopure morpholino β-amino acid from glucose: a new tool for exotic peptide architectures.

Characterization of intrinsically disordered proteins and their dynamic complexes: From in vitro to cell-like environments

Over the last two decades, it has become increasingly clear that a large fraction of the human proteome is intrinsically disordered or contains disordered segments of significant length. These intrinsically disordered proteins (IDPs) play important regulatory roles throughout biology, underlining the importance of understanding their conformational behavior and interaction mechanisms at the molecular level. Here we review recent progress in the NMR characterization of the structure and dynamics of IDPs in various functional states and environments. We describe the complementarity of different NMR parameters for quantifying the conformational propensities of IDPs in their isolated and phosphorylated states, and we discuss the challenges associated with obtaining structural models of dynamic protein-protein complexes involving IDPs. In addition, we review recent progress in understanding the conformational behavior of IDPs in cell-like environments such as in the presence of crowding agents, in membrane-less organelles and in the complex environment of the human cell.

Developing a molecular dynamics force field for both folded and disordered protein states

Many proteins that perform important biological functions are completely or partially disordered under physiological conditions. Molecular dynamics simulations could be a powerful tool for the structural characterization of such proteins, but it has been unclear whether the physical models (force fields) used in simulations are sufficiently accurate. Here, we systematically compare the accuracy of a number of different force fields in simulations of both ordered and disordered proteins, finding that each force field has strengths and limitations. We then describe a force field that substantially improves on the state-of-the-art accuracy for simulations of disordered proteins without sacrificing accuracy for folded proteins, thus broadening the range of biological systems amenable to molecular dynamics simulations.

Molecular dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any physical model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the-art force fields, and compare the results to over 9,000 available experimental data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with experiment for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biological systems amenable to MD simulation. A similar approach could be taken to improve other force fields.

Utilizing dipole-dipole cross-correlated relaxation for the measurement of angles between pairs of opposing CαHα-CαHα bonds in anti-parallel β-sheets

Dipole-dipole cross-correlated relaxation (CCR) between two spin pairs is rich with macromolecular structural and dynamic information on inter-nuclear bond vectors. Measurement of short range dipolar CCR rates has been demonstrated for a variety of inter-nuclear vector spin pairs in proteins and nucleic acids, where the multiple quantum coherence necessary for observing the CCR rate is created by through-bond scalar coupling. In principle, CCR rates can be measured for any pair of inter-nuclear vectors where coherence can be generated between one spin of each spin pair, regardless of both the distance between the two spin pairs and the distance of the two spins forming the multiple quantum coherence. In practice, however, long range CCR (lrCCR) rates are challenging to measure due to difficulties in linking spatially distant spin pairs. By utilizing through-space relaxation allowed coherence transfer (RACT), we have developed a new method for the measurement of lrCCR rates involving CαHα bonds on opposing anti-parallel β-strands. The resulting lrCCR rates are straightforward to interpret since only the angle between the two vectors modulates the strength of the interference effect. We applied our lrCCR measurement to the third immunoglobulin-binding domain of the streptococcal protein G (GB3) and utilize published NMR ensembles and static NMR/X-ray structures to highlight the relationship between the lrCCR rates and the CαHα-CαHα inter-bond angle and bond mobility. Furthermore, we employ the lrCCR rates to guide the selection of sub-ensembles from the published NMR ensembles for enhancing the structural and dynamic interpretation of the data. We foresee this methodology for measuring lrCCR rates as improving the generation of structural ensembles by providing highly accurate details concerning the orientation of CαHα bonds on opposing anti-parallel β-strands.

The templation effect as a driving force for the self-assembly of hydrogen-bonded peptidic capsules in competitive media

Peptide-based cavitands (resorcin[4]arenes substituted with histidine and glutamine hydrazides) exist as monomeric species in polar solvents (DMSO and methanol). Upon complexation of fullerenes, the cavitands wrap around the hydrophobic guests forming dimeric capsular shells (as evidenced by DOSY). The self-assembly of the cavitands is based on the formation of beta-sheet-like binding motifs around the hydrophobic core. In a polar environment, these hydrogen bonded structures are kinetically stable and highly ordered as manifested by a 100-fold increase of intensity of circular dichroism bands, as well as a separate set of signals and substantial differences in chemical shifts in NMR spectra. This behavior resembles a protein folding process at the molten globule stage with non-specific hydrophobic interactions creating a protective and favourable local environment for the formation of secondary structures of proteins.

Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data

Implementation of a new algorithm, SMILE, is described for reconstruction of non-uniformly sampled two-, three- and four-dimensional NMR data, which takes advantage of the known phases of the NMR spectrum and the exponential decay of underlying time domain signals. The method is very robust with respect to the chosen sampling protocol and, in its default mode, also extends the truncated time domain signals by a modest amount of non-sampled zeros. SMILE can likewise be used to extend conventional uniformly sampled data, as an effective multidimensional alternative to linear prediction. The program is provided as a plug-in to the widely used NMRPipe software suite, and can be used with default parameters for mainstream application, or with user control over the iterative process to possibly further improve reconstruction quality and to lower the demand on computational resources. For large data sets, the method is robust and demonstrated for sparsities down to ca 1%, and final all-real spectral sizes as large as 300 Gb. Comparison between fully sampled, conventionally processed spectra and randomly selected NUS subsets of this data shows that the reconstruction quality approaches the theoretical limit in terms of peak position fidelity and intensity. SMILE essentially removes the noise-like appearance associated with the point-spread function of signals that are a default of five-fold above the noise level, but impacts the actual thermal noise in the NMR spectra only minimally. Therefore, the appearance and interpretation of SMILE-reconstructed spectra is very similar to that of fully sampled spectra generated by Fourier transformation.

Nuclear Magnetic Resonance Observation of α-Synuclein Membrane Interaction by Monitoring the Acetylation Reactivity of Its Lysine Side Chains

The interaction between α-synuclein (αS) protein and lipid membranes is key to its role in synaptic vesicle homeostasis and plays a role in initiating fibril formation, which is implicated in Parkinson’s disease. The natural state of αS inside the cell is generally believed to be intrinsically disordered, but chemical cross-linking experiments provided evidence of a tetrameric arrangement, which was reported to be rich in α-helical secondary structure based on circular dichroism (CD). Cross-linking relies on chemical modification of the protein’s Lys C^ε amino groups, commonly by glutaraldehyde, or by disuccinimidyl glutarate (DSG), with the latter agent preferred for cellular assays. We used ultra-high-resolution homonuclear decoupled nuclear magnetic resonance experiments to probe the reactivity of the 15 αS Lys residues toward N-succinimidyl acetate, effectively half the DSG cross-linker, which results in acetylation of Lys. The intensities of both side chain and backbone amide signals of acetylated Lys residues provide direct information about the reactivity, showing a difference of a factor of 2.5 between the most reactive (K6) and the least reactive (K102) residue. The presence of phospholipid vesicles decreases reactivity of most Lys residues by up to an order of magnitude at high lipid:protein stoichiometries (500:1), but only weakly at low ratios. The decrease in Lys reactivity is found to be impacted by lipid composition, even for vesicles that yield similar αS CD signatures. Our data provide new insight into the αS–bilayer interaction, including the pivotal state in which the available lipid surface is limited. Protection of Lys C^ε amino groups by αS–bilayer interaction will strongly impact quantitative interpretation of DSG cross-linking experiments.

Direct Investigation of Slow Correlated Dynamics in Proteins via Dipolar Interactions

The synchronization of native state motions as they transition between microstates influences catalysis kinetics, mediates allosteric interactions, and reduces the conformational entropy of proteins. However, it has proven difficult to describe native microstates because they are usually minimally frustrated and may interconvert on the micro- to millisecond time scale. Direct observation of concerted equilibrium fluctuations would therefore be an important tool for describing protein native states. Here we propose a strategy that relates NMR cross-correlated relaxation (CCR) rates between dipolar interactions to residual dipolar couplings (RDCs) of individual consecutive H(N)-N and H(α)-C(α) bonds, which act as a proxy for the peptide planes and the side chains, respectively. Using Xplor-NIH ensemble structure calculations restrained with the RDC and CCR data, we observe collective motions on time scales slower than nanoseconds in the backbone for GB3. To directly access the correlations from CCR, we develop a structure-free data analysis. The resulting dynamic correlation map is consistent with the ensemble-restrained simulations and reveals a complex network. In general, we find that the bond motions are on average slightly correlated and that the local environment dominates many observations. Despite this, some patterns are typical over entire secondary structure elements. In the β-sheet, nearly all bonds are weakly correlated, and there is an approximately binary alternation in correlation intensity corresponding to the solvent exposure/shielding alternation of the side chains. For α-helices, there is also a weak correlation in the H(N)-N bonds. The degree of correlation involving H(α)-C(α) bonds is directly affected by side-chain fluctuations, whereas loops show complex and nonuniform behavior.

ARTSY-J: Convenient and precise measurement of (3)JHNHα couplings in medium-size proteins from TROSY-HSQC spectra

A new and convenient method, named ARTSY-J, is introduced that permits extraction of the (3)JHNHα couplings in proteins from the relative intensities in a pair of (15)N-(1)H TROSY-HSQC spectra. The pulse scheme includes (3)JHNHα dephasing of the narrower TROSY (1)H(N)-{(15)N} doublet component during a delay, integrated into the regular two-dimensional TROSY-HSQC pulse scheme, and compares the obtained intensity with a reference spectrum where (3)JHNHα dephasing is suppressed. The effect of passive (1)H(α) spin flips downscales the apparent (3)JHNHα coupling by a uniform factor that depends approximately linearly on both the duration of the (3)JHNHα dephasing delay and the (1)H-(1)H cross relaxation rate. Using such a correction factor, which accounts for the effects of both inhomogeneity of the radiofrequency field and (1)H(α) spin flips, agreement between prior and newly measured values for the small model protein GB3 is better than 0.3Hz. Measurement for the HIV-1 protease homodimer (22kDa) yields (3)JHNHα values that agree to better than 0.7Hz with predictions made on the basis of a previously parameterized Karplus equation. Although for Gly residues the two individual (3)JHNHα couplings cannot be extracted from a single set of ARTSY-J spectra, the measurement provides valuable ϕ angle information.

Quantitative evaluation of positive ϕ angle propensity in flexible regions of proteins from three-bond J couplings

(3)JHNHα and (3)JC'C' couplings can be readily measured in isotopically enriched proteins and were shown to contain precise information on the backbone torsion angles, ϕ, sampled in disordered regions of proteins. However, quantitative interpretation of these couplings required the population of conformers with positive ϕ angles to be very small. Here, we demonstrate that this restriction can be removed by measurement of (3)JC'Hα values. Even though the functional forms of the (3)JC'Hα and (3)JHNHα Karplus equations are the same, large differences in their coefficients enable accurate determination of the fraction of time that positive ϕ angles are sampled. A four-dimensional triple resonance HACANH[C'] E.COSY experiment is introduced to simultaneously measure (3)JC'Hα and (3)JHNC' in the typically very congested spectra of disordered proteins. High resolution in these spectra is obtained by non-uniform sampling (in the 0.1-0.5% range). Application to the intrinsically disordered protein α-synuclein shows that while most residues have close-to-zero positive ϕ angle populations, up to 16% positive ϕ population is observed for Asn residues. Positive ϕ angle populations determined with the new approach agree closely with consensus values from protein coil libraries and prior analysis of a large set of other NMR parameters. The combination of (3)JHNC' and (3)JC'C' provides information about the amplitude of ϕ angle dynamics.

How to tackle protein structural data from solution and solid state: An integrated approach

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

Improved Accuracy from Joint X-ray and NMR Refinement of a Protein-RNA Complex Structure

Integrated experimental approaches play an increasingly important role in structural biology, taking advantage of the complementary information provided by different techniques. In particular, the combination of NMR data with X-ray diffraction patterns may provide accurate and precise information about local conformations not available from average-resolution X-ray structures alone. Here, we refined the structure of a ternary protein-protein-RNA complex comprising three domains, Sxl and Unr, bound to a single-stranded region derived in the msl2 mRNA. The joint X-ray and NMR refinement reveals that-despite the poor quality of the fit found for the original structural model-the NMR data can be largely accommodated within the uncertainty in the atom positioning (structural noise) from the primary X-ray data and that the overall domain arrangements and binding interfaces are preserved on passing from the crystalline state to the solution. The refinement highlights local conformational differences, which provide additional information on specific features of the structure. For example, conformational dynamics and heterogeneity observed at the interface between the CSD1 and the Sxl protein components in the ternary complex are revealed by the combination of NMR and crystallographic data. The joint refinement protocol offers unique opportunities to detect structural differences arising from various experimental conditions and reveals static or dynamic differences in the conformation of the biomolecule between the solution and the crystals.

Monomeric Aβ(1-40) and Aβ(1-42) Peptides in Solution Adopt Very Similar Ramachandran Map Distributions That Closely Resemble Random Coil

The pathogenesis of Alzheimer’s disease is characterized by the aggregation and fibrillation of amyloid peptides Aβ^1–40 and Aβ^1–42 into amyloid plaques. Despite strong potential therapeutic interest, the structural pathways associated with the conversion of monomeric Aβ peptides into oligomeric species remain largely unknown. In particular, the higher aggregation propensity and associated toxicity of Aβ^1–42 compared to that of Aβ^1–40 are poorly understood. To explore in detail the structural propensity of the monomeric Aβ^1–40 and Aβ^1–42 peptides in solution, we recorded a large set of nuclear magnetic resonance (NMR) parameters, including chemical shifts, nuclear Overhauser effects (NOEs), and J couplings. Systematic comparisons show that at neutral pH the Aβ^1–40 and Aβ^1–42 peptides populate almost indistinguishable coil-like conformations. Nuclear Overhauser effect spectra collected at very high resolution remove assignment ambiguities and show no long-range NOE contacts. Six sets of backbone J couplings (³J_HNHα, ³J_C′C′, ³J_C′Hα, ¹J_HαCα, ²J_NCα, and ¹J_NCα) recorded for Aβ^1–40 were used as input for the recently developed MERA Ramachandran map analysis, yielding residue-specific backbone ϕ/ψ torsion angle distributions that closely resemble random coil distributions, the absence of a significantly elevated propensity for β-conformations in the C-terminal region of the peptide, and a small but distinct propensity for α_L at K28. Our results suggest that the self-association of Aβ peptides into toxic oligomers is not driven by elevated propensities of the monomeric species to adopt β-strand-like conformations. Instead, the accelerated disappearance of Aβ NMR signals in D₂O over H₂O, particularly pronounced for Aβ^1–42, suggests that intermolecular interactions between the hydrophobic regions of the peptide dominate the aggregation process.

Side Chain Conformational Distributions of a Small Protein Derived from Model-Free Analysis of a Large Set of Residual Dipolar Couplings

Accurate quantitative measurement of structural dispersion in proteins remains a prime challenge to both X-ray crystallography and NMR spectroscopy. Here we use a model-free approach based on measurement of many residual dipolar couplings (RDCs) in differentially orienting aqueous liquid crystalline solutions to obtain the side chain χ₁ distribution sampled by each residue in solution. Applied to the small well-ordered model protein GB3, our approach reveals that the RDC data are compatible with a single narrow distribution of side chain χ₁ angles for only about 40% of the residues. For more than half of the residues, populations greater than 10% for a second rotamer are observed, and four residues require sampling of three rotameric states to fit the RDC data. In virtually all cases, sampled χ₁ values are found to center closely around ideal g^–, g⁺ and t rotameric angles, even though no rotamer restraint is used when deriving the sampled angles. The root-mean-square difference between experimental ³J_HαHβ couplings and those predicted by the Haasnoot-parametrized, motion-adjusted Karplus equation reduces from 2.05 to 0.75 Hz when using the new rotamer analysis instead of the 1.1-Å X-ray structure as input for the dihedral angles. A comparison between observed and predicted ³J_HαHβ values suggests that the root-mean-square amplitude of χ₁ angle fluctuations within a given rotamer well is ca. 20°. The quantitatively defined side chain rotamer equilibria obtained from our study set new benchmarks for evaluating improved molecular dynamics force fields, and also will enable further development of quantitative relations between side chain chemical shift and structure.

MERA: a webserver for evaluating backbone torsion angle distributions in dynamic and disordered proteins from NMR data

MERA (Maximum Entropy Ramachandran map Analysis from NMR data) is a new webserver that generates residue-by-residue Ramachandran map distributions for disordered proteins or disordered regions in proteins on the basis of experimental NMR parameters. As input data, the program currently utilizes up to 12 different parameters. These include three different types of short-range NOEs, three types of backbone chemical shifts ((15)N, (13)C(α), and (13)C'), six types of J couplings ((3)JHNHα, (3)JC'C', (3)JC'Hα, (1)JHαCα, (2)JCαN and (1)JCαN), as well as the (15)N-relaxation derived J(0) spectral density. The Ramachandran map distributions are reported in terms of populations of their 15° × 15° voxels, and an adjustable maximum entropy weight factor is available to ensure that the obtained distributions will not deviate more from a newly derived coil library distribution than required to account for the experimental data. MERA output includes the agreement between each input parameter and its distribution-derived value. As an application, we demonstrate performance of the program for several residues in the intrinsically disordered protein α-synuclein, as well as for several static and dynamic residues in the folded protein GB3.

Quantitative residue-specific protein backbone torsion angle dynamics from concerted measurement of 3J couplings

Three-bond (3)J(C'C') and (3)J(HNHα) couplings in peptides and proteins are functions of the intervening backbone torsion angle ϕ. In well-ordered regions, (3)J(HNHα) is tightly correlated with (3)J(C'C'), but the presence of large ϕ angle fluctuations differentially affects the two types of couplings. Assuming the ϕ angles follow a Gaussian distribution, the width of this distribution can be extracted from (3)J(C'C') and (3)J(HNHα), as demonstrated for the folded proteins ubiquitin and GB3. In intrinsically disordered proteins, slow transverse relaxation permits measurement of (3)J(C'C') and (3)J(HNH) couplings at very high precision, and impact of factors other than the intervening torsion angle on (3)J will be minimal, making these couplings exceptionally valuable structural reporters. Analysis of α-synuclein yields rather homogeneous widths of 69 ± 6° for the ϕ angle distributions and (3)J(C'C') values that agree well with those of a recent maximum entropy analysis of chemical shifts, J couplings, and (1)H-(1)H NOEs. Data are consistent with a modest (≤30%) population of the polyproline II region.

Pushing the limits of signal resolution to make coupling measurement easier

Novel band selective decoupled pure shift selective refocusing experiments allowed simplification of the measurement of all δ¹H, and J_HH couplings with an ultrahigh spectral resolution in peptides.